We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff functions. Our algorithm exploits an intrinsic relationship between the equilibria of the original nonconvex game and the ones of a convexified counterpart. In practice, Cut-and-Play formulates a series of convex approximations of the game and iteratively refines them with cutting planes and branching operations. Our algorithm does not require convexity or continuity of the player's optimization problems and can be integrated with existing optimization software. We test Cut-and-Play on two families of challenging nonconvex games involving discrete decisions and bilevel problems, and we empirically demonstrate that it efficiently computes equilibria while outperforming existing game-specific algorithms.

翻译：我们提出Cut-and-Play算法，一种用于计算同时非合作博弈中纳什均衡的高效实用算法，其中玩家通过具有可分离支付函数的非凸且可能无界的优化问题进行决策。该算法利用原始非凸博弈均衡与凸化对应博弈均衡之间的内在关系。具体而言，Cut-and-Play算法构建一系列博弈的凸近似，并通过切割平面和分支操作迭代细化这些近似。该算法不要求玩家优化问题的凸性或连续性，且可与现有优化软件集成。我们针对两类具有挑战性的非凸博弈（涉及离散决策和双层问题）测试Cut-and-Play算法，实验表明该算法在高效计算均衡的同时，优于现有博弈专用算法。